Chapter 14, Problem 17CPE

To determine

Tofind: the volume and lateral area of cone.

Answer to Problem 17CPE

The volume of cone is $324\pi$ and lateral area of cone is $135\pi$ .

Explanation of Solution

Given information:

Cone radius is $9$ and slant height is $15$ .

Calculation: to find the lateral area of the cone, find the perimeter of cone base and multiply by height,

$\begin{array}{l}L.A.=\pi r\left(h\right)\\ L.A.=\pi \left(9\right)\left(15\right)\text{ [substitute]}\\ L.A.=135\pi \text{ [multiply]}\end{array}$

To find the volume of the cone, multiply the base area by height,

$\begin{array}{l}v=\frac{1}{3}\pi r^{2}h\\ v=\frac{1}{3}\pi {\left(9\right)}^2\left(\sqrt{{\left(15\right)}^2-{\left(9\right)}^2}\right)\text{ [substitute]}\\ v=\frac{1}{3}\pi \left(81\right)\left(12\right)\text{ [simplify]}\\ v=324\pi \text{ [simplify]}\end{array}$